If I cut something into 3 equal pieces, there are 3 defined pieces. But, 1÷3= .333333~. Why is the math a nonstop repeating decimal when existence allows 3 pieces? Is the assumption that it’s physically impossible to cut something into 3 perfectly even pieces?

Question

If I cut something into 3 equal pieces, there are 3 defined pieces. But, 1÷3= .333333~. Why is the math a nonstop repeating decimal when existence allows 3 pieces? Is the assumption that it’s physically impossible to cut something into 3 perfectly even pieces?

In: Mathematics

Answer 1

Just because it’s a non-stop repeating decimal, it’s still a rational number because it can still be expressed as a fraction.

0.3 repeating can be written as 1/3.

This also forms the basis for one of the easier proofs that .9 repeating = 1

1/3 + 1/3 + 1/3 = 3/3 = 1

.333333333333 + .333333333333 +.333333333333 = .9999999999999 = 1